000			04616nam a22004933i 4500
001			EBC4901863
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005			20240729131324.0
006			m o d |
007			cr cnu||||||||
008			240724s2016 xx o ||||0 eng d
020			_a9781470429423 _q(electronic bk.)
020			_z9781470419264
035			_a(MiAaPQ)EBC4901863
035			_a(Au-PeEL)EBL4901863
035			_a(OCoLC)948030438
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA242 .M86 2016
082	0		_a512.7/4
100	1		_aMoriwaki, Atsushi.
245	1	0	_aAdelic Divisors on Arithmetic Varieties.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2016.
264		4	_c©2016.
300			_a1 online resource (134 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.242
505	0		_aCover -- Title page -- Introduction -- 0.1. Birational Arakelov geometry -- 0.2. Green functions on analytic spaces over a compete discrete valuation field -- 0.3. Adelic arithmetic divisors -- 0.4. Main results -- 0.5. Conventions and terminology -- Chapter 1. Preliminaries -- 1.1. Lemmas -- 1.2. ℝ-Cartier divisors on a noetherian integral scheme -- 1.3. Analytification of algebraic schemes over a complete valuation field -- 1.4. Green functions on complex varieties -- Chapter 2. Adelic ℝ-Cartier Divisors over a Discrete Valuation Field -- 2.1. Green functions on analytic spaces over a discrete valuation field -- 2.2. Definition of adelic ℝ-Cartier divisors -- 2.3. Local degree -- 2.4. Local intersection number -- Chapter 3. Local and Global Density Theorems -- 3.1. Vertical fractional ideal sheaves and birational system of models -- 3.2. Model functions -- 3.3. Density theorems -- 3.4. Zariski's lemma for integrable functions -- 3.5. Radon measure arising from local intersection number -- Chapter 4. Adelic Arithmetic ℝ-Cartier Divisors -- 4.1. Definition and basic properties -- 4.2. Global degree -- 4.3. Volume of adelic arithmetic ℝ-Cartier divisors -- 4.4. Positivity of adelic arithmetic ℝ-Cartier divisors -- 4.5. Global intersection number -- Chapter 5. Continuity of the Volume Function -- 5.1. Basic properties of the volume -- 5.2. Proof of the continuity of the volume function -- 5.3. Applications -- Chapter 6. Zariski Decompositions of Adelic Arithmetic Divisors on Arithmetic Surfaces -- 6.1. Local Zariski decompositions of adelic divisors on algebraic curves -- 6.2. Proof of Zariski decompositions for adelic arithmetic divisors -- Chapter 7. Characterization of Nef Adelic Arithmetic Divisors on Arithmetic Surfaces -- 7.1. Hodge index theorem for adelic arithmetic divisors -- 7.2. Arithmetic asymptotic multiplicity.
505	8		_a7.3. Necessary condition for the equality ̂ =̂ ᵪ -- 7.4. Numerical characterization -- Chapter 8. Dirichlet's unit Theorem for Adelic Arithmetic Divisors -- 8.1. Fundamental question for adelic divisors -- 8.2. Proof of Theorem 8.1.2 -- Appendix A. Characterization of Relatively Nef Cartier Divisors -- A.1. Asymptotic multiplicity -- A.2. Sectional decomposition -- A.3. Characterization in terms of _{ } -- Bibliography -- Subject Index -- Symbol Index -- Back Cover.
520			_aIn this article, the author generalizes several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors, Zariski decompositions for arithmetic divisors on arithmetic surfaces and a special case of Dirichlet's unit theorem on arithmetic varieties, to the case of the adelic arithmetic divisors.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aDivisor theory.
650		0	_aTopological groups.
650		0	_aAlgebraic varieties.
650		0	_aApproximation theory.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aMoriwaki, Atsushi _tAdelic Divisors on Arithmetic Varieties _dProvidence : American Mathematical Society,c2016 _z9781470419264
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901863 _zClick to View
999			_c127899 _d127899